Numbersystem, some clarification
10th Nov 1998 Kailash Srivastava @mail.bip.net
On http://www.freeindia.org/home.shtml, I found the following: >Mathematics : Number system including zero, all basic mathematics >including algebra, arithmetic, trigonometry, geometry > It is claimed to be one of the Indian achievements. Is it correct that the number system was given by Indians? If yes, why do we call them Arabic numbers? Kailash Srivastava
10th Nov 1998 Vivek Murarka @manaskriti.com
> >Mathematics : Number system including zero, all basic mathematics > >including algebra, arithmetic, trigonometry, geometry <> > It is claimed to be one of the Indian achievements. > > Is it correct that the number system was given by Indians? If yes, why do > we call them Arabic numbers? *We* call them that because, and when, we communicate in English. Yes, it is a fact that Indian mathematicians developed the number system in the pre Greek/Roman era. The conceptualisation of, and the mathematical symbolisation of, the Zero particularly is acknowledged to be the gift of India. Sometime since the visit of Alexander the Great, this number system reached Arabia/Asia Minor. With the Moor Invasion of Europe, and the Crusades, the number system reached Europe. Since the Europeans got it from the Arabs, it became know to them as the Arabic Numerals. Until then, Europe used the Roman numbering system (which is based on the Roman Script/alphabet) where the progression is somewhat clumsy in comparison to the Arabic. So that the denotation of larger numbers becomes almost messy. And note that there is no zero used in the Roman numbering system - even though it too is a decimal system. BTW one of the Upnishads (the Easopnishad I believe) begins with the sloka : Om prunamadah purnamidam purnat purnamuddachayate Purnasya purnmadaya purnamevavashishyate. That is the first, most enduring, and most concise definition/descriptio of Infinity - both Divine and mathematical. Hope this helps. Please excuse me for two things : 1. I dont know Sanskrit, so there may be mistakes, and I cant translate. 2. The basic facts are correct, but I may be wrong in some of the details. Will someone help us with both. Regards, Vivek
12th Nov 1998 vijay @wmi.co.in
I was very happy to see your reply , it is sad that in my own country there are people who believe that science started with Newton. Without his discoveries that refindings we the Indians would not have been educated. Your Hymn means that when add fullness i.e. zero or completeness to zero, it adds up to Zero and when you remove zero from zero what remains is Zero. It means that there is only one universe (completeness)and even when you add or subtract itself from it, it remains the same. Because it is complete in all respect. Arabs were wanderers and needed the knowledge of stars and maths for finding their ways in the desert. They got both from us the Indians. The rest of the Europe whom we are aping today was a barbaric community and they got this all from Arabs at a later date. So be informed about your nations language which is the richest in the whole world and the heritage which is so deep that no on will ever match it Our ancestors did not believe in making much of themselves.
12th Nov 1998 Aditya, the Hindu Skeptic @bc.seflin.org
On 12 Nov 98, Vivek Murarka wrote: > got it from the Arabs, it became know to them as the Arabic > Numerals. Incidentally the Arabs themselves do acknowledge Indian origin of numeral system and the word for numeral in Arabic is Hindsa i.e. Indian symbol. Secondly as many of you know Arabic is written from right to left unlike Hindi and most European languages but the numbers are written from left to right just the way it was being done in India at the time. > Until then, Europe used the Roman numbering system (which is > based on the Roman Script/alphabet) where the progression is > somewhat clumsy in comparison to the Arabic. So that the > denotation of larger numbers becomes almost messy. And note that > there is no zero used in the Roman numbering system - even > though it too is a decimal system. Decimal system was actually a very poor choice and we are unfortunately stuck with it. The other system known to coexist is sexadecimal (60) that is still used in time and angle measurements. It did not become very popular due to unwieldily large base. The best would have been a duodecimal system since it has many more natural factors and fractions could be written and worked out more conveniently. Duodecimal system was also prevalent in India in zodiac symbols and as its corollary the number o months in a year etc.. I wish the Indians had integrated the two systems before they became universally accepted. It was left for the French revolutionaries to reorganize the hodge podge of number systems and units which resulted in the Metric system which was at least coherent though not optimum. > Om prunamadah purnamidam purnat purnamuddachayate > Purnasya purnmadaya purnamevavashishyate. > > That is the first, most enduring, and most concise > definition/descriptio of Infinity - both Divine and mathematical. This definition actually applies to zero and infinity both and actually shows the principle of duality. One can say therefore say that anything infinite is tantamount to it being nonexistent. Therefore the concepts of zero and infinity are complement of each other. When the Indian mathematician or philosopher stumbled on the idea of zero, he also gave birth to the concept of infinity.
13th Nov 1998 Kerry R Kinchen @stic.net
>>Mathematics : Number system including zero, >>It is claimed to be one of the Indian achievements. >...Yes, it is a fact that Indian mathematicians developed the number system in the pre Greek/Roman era. The conceptualisation of, and the mathematical symbolisation of, the Zero particularly is acknowledged to be the gift of India. >...The basic facts are correct, but I may be wrong in some of the details. Will someone help us with both? Hello all, Maybe this will be of some help: "The ancient Mayans were the first to introduce the concept of zero as a number, centuries ago." Quoted from Dr. Lewis also known as "Dr. Math" http://forum.swarthmore.edu/dr.math/problems/greeno188.8.131.52.html "The Babylonians used written symbols for numbers thousands of years before they invented a symbol for zero. Zero was introduced initially, not as a number to be used in computation, but as a position marker to distinguish between such numbers as 123, 1203, 1230, and 1023. The Maya, about the 1st century AD, used a small oval containing an inner arc to denote zero. About five centuries later Indian Mathematicians began to use a circle or a dot as a symbol for zero; the dot later fell into disuse. These Indian mathematicians wrote numbers in columns, and they used the zero to represent a blank column. The Hindu word for zero was sunya, meaning empty, or void; this word, translated and transliterated by the Arabs as sifr, is the root of the English words cipher and zero." Quoted entry by two mathematicians in the Funk & Wagnells Encyclopedia of 1998 JAMES SINGER, M.A., Ph.D. Late Professor Emeritus of Mathematics, Brooklyn College of the City University of New York. Author of Elements of Numerical Analysis. J. LENNART BERGGREN, M.S., Ph.D. Professor of Mathematics and Statistics, Simon Fraser University. Author of Mathematics in Medieval Islam. Thanks, Kerry Kinchen email@example.com
15th Nov 1998 Vivek Murarka @manaskriti.com
Dear Netters & IINNers, As I had said, the basic facts are correct. The conceptualisation of Zero and Infinity are India's gifts to Humanity. And as Aditya said, Zero and Infinity bring us Full Circle (pun intended - though it came as I was writing). I will not argue with the facts Kerry has presented, until I have researched them, to the extent as a non-mathematician I can. But, as I said, the original conceptualisation was Indian. As Mr Sudheer Birodkar notes in his book (from which the subject line of this msg is borrowed), the concept of "Shunya" is is too old in Ancient Indian Texts to be dated. And it is a concept which, ab initio - from the time of its conceptualisation, covers the subsidiary concepts of nothingness/emptiness/zero/infinity/fullness/space/universe/atmos phere .... . Please visit the book's website at : http://india.coolatlanta.com/GreatPages/sudheer/index.html It was Kerry's mail which stimulated me to do a short Excite search which threw up above URL. The Search also threw up http://aleph0.clarku.edu/~djoyce/mathhist/. The India related links on this site are credited to Srinivas Padmanabhuni - who I believe is a fellow IINN mate. And http://www-history.mcs.st-and.ac.uk/~history/ was the a very valuable resource find for me. But for sites on Mayan & Babylonian mathematics, I think I'll have to search further. So until then ... Regards, Vivek Murarka
16th Nov 1998 P srini @hotmail.com
Hi With reference to the discussion of invention of zero, it appears that there is little doubt as to the invention of zero in the current form was attributed to Indians. But as to its invention as an entity there appears to be three different independent sources of such invention (Source: From Zero to One, A universal history of numbers, Georges Ifrah, Viking Publishers). (1). The most ancient of them was around two millenia before christ by the Babylonians. In their digit system there were two group of tally marks to identify numbers the tens, and the ones. And the system was sexagesimal. They had a tough time to identify the notion of "nothing" in a place , and for centuries they used to leave a space for such a place. later a special symbol was devised around fourth century BC. This was never though used as a number and was used a symbol for "nothingness". (2). Apparently the Mayans used a similar concept of zero to represent nothingness in thir number system which wass also having the concept of place value based on base 20. But the number symbol for zero apparently had not operativepossibilites other than being used to represent nothingness. timing is considered around fourth to sixth century AD. more info at http://www.interlochen.k12.mi.us/Math/IndianMath/mayamathsystem.html 3). The following excerpt best explains the most probable source of zero as we know it. >From : The HINDU-ARABIC NUMERALS by DAVID EUGENE SMITH and LOUIS CHARLES KARPINSKI boston and london ginn and company,publishers 1911. The earliest undoubted occurence of a zero in India is an inscription at Gwalior, dated Samvat 933 (876 AD), where 50 garlands are mentioned. 270 is written as the current day 270 in Hindi. Apart from its appearance in early inscriptions, there is still another indication of the Hindu origin of the symbol in the special treatment of the concept zero in the early works of arithmetic.Brahmagupta who lived in Ujjain the centre of indian astronomy in the early part of the seventh century gives in his arithmetic a distinct treatment of the properties of zero. He showed a special significance for zero unlike Greek or other ancient arithmetics. A similar scientific treatment is given by bhaskara, although he permitted division by zero. Similarly the Ganita-Sara-sangraha of Mahaviracarya(830 AD) discusses calculation of zero although it does not discuss a place value system with zero. The dot, which the Hindus used to fill up lacunae in their manuscripts was the was the natural symbol. Bakhsali script, the word sunya, with dot as symbol was used to denote zero. Although the dot was first used in India, the small circle replaced it and continues to be used today. The sunya of Hindus was passed over to the Arabic as al-sifr or sifr. From al-sifr came zephyr,cipher an finally the abridged form zero. The earliest printed work found in the fnal form of today was in the Calindri's arithmetic of 1491. -------------------------------------- -srinivas padmanabhuni Web Architect http://www.samilan.com - Home of SAIR, biggest search engine for India